DUAL NATURE OF MATTER AND RADIATION

DUAL NATURE OF MATTER AND

RADIATIONWAVE +PARTICLE =WAVICLES

PHOTOELECTRIC EFFECT

The Phenomenon explaining particle nature of light.

BECAUSE METALS HAVE FREE ELECTRONS.

EMISSION OF ELECTRONS FROM METALS, WHY?

NO

Do these free electrons are so free as to come out of the metal on their own?

Because these electrons are strongly attracted by the group of positive ions inside.

It is remarkable that these positive ions are formed only when the electrons of the outermost orbit(now free electrons) leave the atom.

Hence some energy is required to take out these so called free electrons

On this basis(source of energy) electron emission is of following types.

WHY?

THERMIONIC EMISSION Emission of electrons by heat energy. ELECTRIC FIELD EMISSION – Emission of electrons by applying electric

field. PHOTOELECTRIC EMISSION – Emission of electrons due to photons(i.e.

light of suitable frequency.)

TYPES OF ELECTRON EMISSION

The energy required to take out electron from the metal surface.

WORK FUNCTION φ

PHOTOELECTRIC EMISSION

Thus incidence of light of suitable frequency on a metal surface causes the emission of electrons. The phenomenon is known as photoelectric emission & the electrons are known as photoelectrons. If these electrons are directed in such a way so as to obtain current then this is known as photoelectric current.

The wavy lines represent light.

Experimental set up-

Incident light triggers the emission of (photo)electrons from the cathode• Some of them travel toward the collector (anode) with an initial kineticenergy• The applied voltage V either accelerates (if positive) or decelerates (ifnegative) the incoming electrons.• The intensity I of the current measured by the ammeter as a function of theapplied voltage V is a measurement of the photoelectron properties, andtherefore a measurement of the properties of the photoelectric effect.

Intensity of incident light – On increasing the intensity of incident light

photoelectric current increased.

Observations of Lenard & Millikan-

Photoelectric current α Intensity of incident light.

For the potential increased from zero to some positive value the photoelectric current increased as it attracted more & more electrons.

For negative potential i.e. Retarding potential applied on the collector the photoelectric current decreased gradually.

At a certain value of negative potential the photoelectric current became zero. This is called as Stopping or Cut off potential.

Potential applied at the collector-

i.e. Kmax = eV0 ( v =w/q)

Here V0 is stopping potential.

This stopping potential is a measure of maximum K.E. of electrons.

At the stopping potential when intensity was increased no current was obtained.

This implies that increasing intensity does not give so much courage (energy) to the electrons so as to overcome the barrier posed by retarding potential i.e. to say

Intensity is not related to energy

Effect of Intensity at Stopping Potential-

At the stopping potential when frequency of light was increased current was obtained.

This implies that frequency must have increased the energy of electrons.

On studying the variation between frequency of incident light & K.E. of emitted electrons the following graph was obtained.

Effect of frequency of light-

Frequency vs Retarding Potential i.e. a measure of max. K.E.

For every metal there exists a certain frequency below which emission of electrons cannot occur known as threshold frequency.

At this frequency the K.E. of emitted electrons is zero.

The graph for different metals are parallel straight lines implying that the slope of the graph must be a universal constant.

Taking analogy of the equation – y = mx+c Equation of straight line in the graph can be

Conclusions from graph

where E represents energy on y axis ν represents frequency on x axis. B is the intercept of the graph on y axis.

E = Aν-B

The no. of photoelectrons emitted is directly proportional to the intensity of incident light.

The energy of photoelectrons does not depend upon intensity of light.

The energy of electrons is directly proportional to the frequency of incident light.

There exists a certain minimum frequency below which electron emission does not occur known as threshold frequency.

Laws of Photoelectric Emission

There is no time lag between the incidence of photons & emission of electrons.

Laws Contd.

The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.

The photoelectric effect should occur for any light, regardless of frequency or wavelength.

There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.

Failure of wave theory

What is Quantum Theory?Quantum theory is a theory needed to describe physics on amicroscopic scale, such as on the scale of atoms, molecules,electrons, protons, etc.

Classical theories: Newton – Mechanical motion of objects (F = ma) Maxwell – Light treated as a wave

Quantum (from Merriam-Webster) Any of the very small increments or parcels into which many forms of energy are subdivided.

Light is a form of energy is a quantum of EM energy

Photons Quantum theory describes light as a particle called a photon

According to quantum theory, a photon has an energy given by

E = hn = hc/l h = 6.6x10-34 [J s] Planck’s constant, after the scientist Max Planck.

The energy of the light is proportional to the frequency (inversely proportional to the wavelength) ! The higher the frequency (lower wavelength) the higher the energy of the photon.

A photon’s energy(hν) is used in two ways- Energy required to take the electron out of

the metal surface(work function W) Energy left is the K.E. of the electron

emitted. Mathematically- hν = W + K.E. Here W represents the minimum energy

required to take out electron from the metal surface. Hence from quantum theory

W =hν0

Einstein’s explanation-

Thus hν = hν0 + 1/2mv2 1/2mv2 = h(ν - ν0 ) This is Einstein’s Photoelectric equation. On the basis of this equation the laws of

photoelectric emission can be explained- As it is clear from the above equation energy of

electrons emitted depends upon the frequency of incident light & not upon intensity.

If ν < ν0 then K.E. will be negative i.e. impossible,hence emission of electrons below threshold frequency is not possible.

Where ν0 represents threshold frequency.

How does this explain the photoelectric effect?

Think about hitting a ball into outer space. If you don't hit it hard enough, it will just come back

down. No matter how many times you hit it. If superman hit it, he could get it into space. Similarly, no matter how many photons strike the

metal, if none of them has sufficient energy to eject an electron from a metal atom, you won't get a current.

If the energy the taken up by the electron is sufficient to allow it to be released from the metal atom, you will get a current.

Also photoelectric emission is an instantaneous phenomenon. The moment light is made incident on metal surface , photon is absorbed by the electron & it comes out. Hence there is no time lag.

Exp Contd.

Summary of Photons

Photons can be treated as “packets of light” which behave as a particle.

To describe interactions of light with matter, one generally has to appeal to the particle (quantum) description of light.

A single photon has an energy given by E = hc/l,

where h = Planck’s constant = 6.6x10-34 [J s] and, c = speed of light = 3x108 [m/s] l = wavelength of the light (in [m])

Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/l

Photons can be treated as “packets of light” which behave as a particle.

To describe interactions of light with matter, one generally has to appeal to the particle (quantum) description of light.

A single photon has an energy given by E = hc/l,

where h = Planck’s constant = 6.6x10-34 [J s] and, c = speed of light = 3x108 [m/s] l = wavelength of the light (in [m])

Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/l

So is light a wave or a particle ?

On macroscopic scales, we can treat a large number of photonsas a wave.

When dealing with subatomic phenomenon, we are often dealingwith a single photon, or a few. In this case, you cannot usethe wave description of light. It doesn’t work !

De Broglie generalized the idea of dual nature of radiation to matter.

Dual nature of matter

Light has a dual nature___________________________ Wave (electromagnetic) - Interference - Diffraction Particle (photons) - Photoelectric effect - Compton effect

Wave - Particle Duality for light

What about Matter?_______________________________ If light, which was traditionally understood

as a wave also turns out to have a particle nature, might matter, which is traditionally understood as particles, also have a wave nature?

Yes!

Louis de Broglie’s hypothesis____________________________

The dual nature of matter A particle with momentum p has a matter

wave associated with it, whose wavelength is given by

p

h

The connecting link – Planck’s constant_______________________________

Dual Nature

Radiation

Matter

hE

p

h

Why isn’t the wave nature of matter more apparent to us…?___________________________________

Planck’s constant is so small that we don’t observe the wave behaviour of ordinary objects – their de Broglie wavelengths could be many orders of magnitude smaller than the size of a nucleus!

J.s10x6.6 34h

Particle______________________________

Our traditional understanding of a particle…

“Localized” - definite position, momentum, confined in space

Wave____________________________ Our traditional understanding of a wave….

“de-localized” – spread out in space and time

How do we associate a wave nature to a particle?___________________________________

What could represent both wave and

particle? • Find a description of a particle which is

consistent with our notion of both particles and waves……

Fits the “wave” description

“Localized” in space

____________________________________

A “Wave Packet”

How do you construct a wave

packet?

Constructing a wave packet by adding up several waves …………___________________________________If several waves of different wavelengths (frequencies) and phases are superposed together, one would get a resultant which is a localized wave packet

Heisenberg's Uncertainty Principle___________________________________ The Uncertainty Principle is an important

consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature

Simply stated, it is impossible to know both the exact position and the exact momentum of an object simultaneously

A fact of Nature!

A wave packet describes a

particle

____________________________ A wave packet is a group of waves with

slightly different wavelengths interfering with one another in a way that the amplitude of the group (envelope) is non-zero only in the neighbourhood of the particle

A wave packet is localized – a good representation for a particle!

Heisenberg's Uncertainty Principle__________________________________

Uncertainty in Position :

Uncertainty in Momentum:

x

xp

2

hpx x

Uncertainty Principle and the Wave Packet___________________________________

p

h

2

hpx x

If is large, is small

p

p

x

x

Summary___________________________________

Matter and radiation have a dual nature – of both wave and particle

The matter wave associated with a particle has a de Broglie wavelength given by

p

h

Davisson-Germer Experiment If particles have a wave nature, then under

appropriate conditions, they should exhibit diffraction

Davisson and Germer measured the wavelength of electrons

This provided experimental confirmation of the matter waves proposed by de Broglie

Davisson and Germer Experiment Electrons were

directed onto nickel crystals

Accelerating voltage is used to control electron energy: E = |e|V

The scattering angle and intensity (electron current) are detected◦ φ is the scattering

angle

Davisson and Germer Experiment If electrons are “just” particles, we expect a

smooth monotonic dependence of scattered intensity on angle and voltage because only elastic collisions are involved

Diffraction pattern similar to X-rays would be observed if electrons behave as waves

Davisson and Germer Experiment

Davisson and Germer Experiment Observations:

◦ Intensity was stronger for certain angles for specific accelerating voltages (i.e. for specific electron energies)

◦ Electrons were reflected in almost the same way that X-rays of comparable wavelength

Davisson and Germer Experiment Observations:

◦Current vs accelerating voltage has a maximum, i.e. the highest number of electrons is scattered in a specific direction

◦This can’t be explained by particle-like nature of electrons electrons scattered on crystals behave as wavesFor φ ~ 50° the maximum is at ~54V

Davisson and Germer Experiment For X-ray Diffraction on Nickel

5065

A65.1 ;A91.0

sin2o

ray-X

o

111

d

d

Davisson and Germer Experiment (Problem 40.38) Assuming the wave

nature of electrons we can use de Broglie’s approach to calculate wavelengths of a matter wave corresponding to electrons in this experiment

V = 54 V E = 54 eV = 8.64×10-18J

A67.1J106.8kg101.92

sec-J1063.6

2,2,

2

1831

34

2

B

BmE

hmEp

m

pE

This is in excellent agreement with wavelengths of X-rays diffracted from

Nickel!

In previous experiments many electrons were diffracted

Will one get the same result for a single electron?

Such experiment was performed in 1949◦ Intensity of the electron beam was so low that

only one electron at a time “collided” with metal

◦ Still diffraction pattern, and not diffuse scattering, was observed, confirming that

Thus individual electrons behave as waves

Single Electron Diffraction